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When two wrongs make a right: synchronized neuronal bursting from combined electrical and inhibitory coupling. (English) Zbl 1404.92059

Summary: Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. In this paper, we study the emergence of synchronization in networks of bursting neurons as a highly non-trivial, combined effect of electrical and inhibitory connections. We report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism, which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm.

MSC:

92C20 Neural biology
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[1] Churchland PS, Sejnowski TJ. (1994) The computational brain. Cambridge, MA: The MIT Press.
[2] Mizuseki K, Buzsáki G. (2013) Theta oscillations decrease spike synchrony in the hippocampus and entorhinal cortex. Phil. Trans. R. Soc. B 369, 20120530. (doi:10.1098/rstb.2012.0530) · doi:10.1098/rstb.2012.0530
[3] Wolf JA, Koch PF. (2016) Disruption of network synchrony and cognitive dysfunction after traumatic brain injury. Front. Syst. Neurosci. 10, 43. (doi:10.3389/fnsys.2016.00043) · doi:10.3389/fnsys.2016.00043
[4] Netoff I, Schiff J. (2002) Decreased neuronal synchronization during experimental seizures. J. Neurosci. 22, 7297-7307.
[5] Schindler K, Elger C, Lehnertz K. (2007) Increasing synchronization may promote seizure termination: evidence from status epilepticus. Clin. Neurophysiol. 118, 1955-1968. (doi:10.1016/j.clinph.2007.06.006) · doi:10.1016/j.clinph.2007.06.006
[6] Adhikari B, Epstein C, Dhamala M. (2013) Localizing epileptic seizure onsets with Granger causality. Phys. Rev. E 88, 030701. (doi:10.1103/PhysRevE.88.030701) · doi:10.1103/PhysRevE.88.030701
[7] Lehnertz K, Ansmanna G, Bialonski S, Dickten H, Geier C, Porz S. (2014) Evolving networks in the human epileptic brain. Physica D 267, 7-15. (doi:10.1016/j.physd.2013.06.009) · doi:10.1016/j.physd.2013.06.009
[8] Wang X-J, Rinzel J. (1992) Alternating and synchronous rhythms in reciprocally inhibitory model neurons. Neural Comput. 4, 84-97. (doi:10.1162/neco.1992.4.1.84) · doi:10.1162/neco.1992.4.1.84
[9] Somers D, Kopell N. (1993) Rapid synchronization through fast threshold modulation. Biol. Cybern. 68, 393-407. (doi:10.1007/BF00198772) · doi:10.1007/BF00198772
[10] Canavier CC, Baxter DA, Clark JW, Byrne JH. (1999) Control of multistability in ring circuits of oscillators. Biol. Cybern. 80, 87-102. (doi:10.1007/s004220050507) · Zbl 0918.92008 · doi:10.1007/s004220050507
[11] Izhikevich E. (2001) Synchronization of elliptic bursters. SIAM Rev. 43, 315-344. (doi:10.1137/S0036144500382064) · Zbl 0992.92014 · doi:10.1137/S0036144500382064
[12] Dhamala MM, Jirsa V, Ding M. (2004) Transitions to synchrony in coupled bursting neurons. Phys. Rev. Lett. 92, 028101. (doi:10.1103/PhysRevLett.92.028101) · doi:10.1103/PhysRevLett.92.028101
[13] Belykh I, de Lange E, Hasler M. (2005) Synchronization of bursting neurons: what matters in the network topology. Phys. Rev. Lett. 94, 188101. (doi:10.1103/PhysRevLett.94.188101) · doi:10.1103/PhysRevLett.94.188101
[14] Coombes S, Bressloff PC (eds). (2005) Bursting: the genesis of rhythm in the nervous system. Singapore: World Scientific. · Zbl 1094.92500
[15] Neiman AB, Russell DF, Yakusheva TA, DiLullo A, Tass PA. (2007) Response clustering in transient stochastic synchronization of coupled neuronal bursters. Phys. Rev. E 7, 021908. (doi:10.1103/PhysRevE.76.021908) · doi:10.1103/PhysRevE.76.021908
[16] Vicente R, Gollo L, Mirasso C, Fischer I, Pipa G. (2008) Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. Proc. Natl Acad. Sci. USA 105, 17 157-17 162. (doi:10.1073/pnas.0809353105) · doi:10.1073/pnas.0809353105
[17] Belykh I, Hasler M. (2011) Mesoscale and clusters of synchrony in networks of bursting neurons. Chaos 21, 016106. (doi:10.1063/1.3563581) · Zbl 1345.92035 · doi:10.1063/1.3563581
[18] Wojcik J, Clewley R, Schwabedal J, Shilnikov A. (2014) Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. PLoS ONE 9, e92918. (doi:10.1371/journal.pone.0092918) · doi:10.1371/journal.pone.0092918
[19] Gollo L, Mirasso C, Sporns O, Breakspear M. (2014) Mechanisms of zero-lag synchronization in cortical motifs. PLoS Comput. Biol. 10, e1003548. (doi:10.1371/journal.pcbi.1003548) · doi:10.1371/journal.pcbi.1003548
[20] Amigó JM, Mosqueiro TS, Huerta R. (2015) Predicting synchronization of three mutually inhibiting groups of oscillators with strong resetting. Appl. Math. Inf. Sci. 9, 2245-2256. (doi:10.12988/ams.2015.53205) · doi:10.12988/ams.2015.53205
[21] Rinzel J. (1987)A formal classification of bursting mechanisms in excitable systems. In Mathematical topics in population biology, morphogenesis, and neurosciences (eds E Teramoto, M Yamaguti). Lecture Notes in Mathematics, no. 71, pp. 251-291. Berlin, Germany: Springer. · Zbl 0646.92004
[22] Terman D. (1991) Hysteresis dynamics, bursting oscillations and evolution to chaotic regimes. SIAM J. Appl. Dyn. Syst. 51, 1418-1450. (doi:10.1137/0151071) · Zbl 0754.58026 · doi:10.1137/0151071
[23] Izhikevich E. (2000) Neural excitability, spiking, and bursting. Int. J. Bifurc. Chaos 10, 1171-1266. (doi:10.1142/S0218127400000840) · Zbl 1090.92505 · doi:10.1142/S0218127400000840
[24] Krishnan G, Bazhenov M. (2011) Ionic dynamics mediate spontaneous termination of seizures and postictal depression state. J. Neurosci. 24, 8870-8882. (doi:10.1523/JNEUROSCI.6200-10.2011) · doi:10.1523/JNEUROSCI.6200-10.2011
[25] Frohlich F, Bazhenov M. (2006) Coexistence of tonic firing and bursting in cortical neurons. Phys. Rev. E 74, 031922. (doi:10.1103/PhysRevE.74.031922) · doi:10.1103/PhysRevE.74.031922
[26] Skinner FK, Zhang L, Velazquez JL, Carlen PL. (1999) Bursting in inhibitory interneuronal networks: a role for gap-junctional coupling. J. Comput. Neurosci. 81, 1274-1283.
[27] Lewis T, Rinzel J. (2003) Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J. Comput. Neurosci. 14, 283-309. (doi:10.1023/A:1023265027714) · doi:10.1023/A:1023265027714
[28] Best J, Borisyuk A, Rubin J, Terman D, Wechselberger M. (2005) The dynamic range of bursting in a model respiratory pacemaker network. SIAM J. Appl. Dyn. Syst. 4, 1107-1139. (doi:10.1137/050625540) · Zbl 1106.34023 · doi:10.1137/050625540
[29] Belykh I, Shilnikov A. (2008) When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons. Phys. Rev. Lett. 101, 078102. (doi:10.1103/PhysRevLett.101.078102) · doi:10.1103/PhysRevLett.101.078102
[30] Kopell N, Ermentrout B. (2004) Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. Proc. Natl Acad. Sci. USA 101, 15 482-15 487. (doi:10.1073/pnas.0406343101) · doi:10.1073/pnas.0406343101
[31] Pfeuty B, Mato G, Golomb D, Hansel D. (2005) The combined effects of inhibitory and electrical synapses in synchrony. Neural Comput. 17, 633-670. (doi:10.1162/0899766053019917) · Zbl 1059.92012 · doi:10.1162/0899766053019917
[32] Pfeuty B, Golomb D, Mato G, Hansel D. (2007) Inhibition potentiates the synchronizing action of electrical synapses. Front. Comp. Neurosci. 1, 1-8. (doi:10.3389/neuro.10/008.2007) · doi:10.3389/neuro.10/008.2007
[33] Van Vreeswijk C, Abbott LF, Ermentrout GB. (1994) When inhibition not excitation synchronizes neural firing. J. Comput. Neurosci. 1, 313-321. (doi:10.1007/BF00961879) · doi:10.1007/BF00961879
[34] Terman D, Kopell N, Bose A. (1998) Dynamics of two mutually coupled slow inhibitory neurons. Physica D 117, 241-275. (doi:10.1016/S0167-2789(97)00312-6) · Zbl 0941.34027 · doi:10.1016/S0167-2789(97)00312-6
[35] Rubin J, Terman D. (2000) Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comput. 12, 597-645. (doi:10.1162/089976600300015727) · doi:10.1162/089976600300015727
[36] Rubin J, Terman D. (2002) Synchronized activity and loss of synchrony among heterogeneous conditional oscillators. SIAM J. Appl. Dyn. Syst. 1, 146-174. (doi:10.1137/S111111110240323X) · Zbl 1015.34027 · doi:10.1137/S111111110240323X
[37] Elson RC, Selverston AI, Abarbanel HDI, Rabinovich MI. (2002) Inhibitory synchronization of bursting in biological neurons: dependence on synaptic time constant. J. Neurophysiol. 88, 1166.
[38] Jalil S, Belykh I, Shilnikov A. (2010) Fast reciprocal inhibition can synchronize bursting neurons. Phys. Rev. E 81, 045201. (doi:10.1103/PhysRevE.81.045201) · Zbl 1204.92015 · doi:10.1103/PhysRevE.81.045201
[39] Jalil S, Belykh I, Shilnikov A. (2012) Spikes matter for phase-locked bursting in inhibitory neurons. Phys. Rev. E 85, 036214. (doi:10.1103/PhysRevE.85.036214) · doi:10.1103/PhysRevE.85.036214
[40] Reimbayev R, Belykh I. (2014) When transitions between bursting modes induce neural synchrony. Int. J. Bifurc. Chaos 22, 1440013. (doi:10.1142/S0218127414400136) · Zbl 1300.34129 · doi:10.1142/S0218127414400136
[41] Belykh I, Reimbayev R, Zhao K. (2015) Synergistic effect of repulsive inhibition in synchronization of excitatory networks. Phys. Rev. E 91, 062919. (doi:10.1103/PhysRevE.91.062919) · doi:10.1103/PhysRevE.91.062919
[42] Kita H, Kosaka T, Heizman C. (1990) Parvalbumin-immunoreactive neurons in the rat neostriatum: a light and electron microscopic study. Brain Res. 536, 1-15. (doi:10.1016/0006-8993(90)90002-S) · doi:10.1016/0006-8993(90)90002-S
[43] Gibson JR, Beierlein M, Connors BW. (1999) Two networks of electrically coupled inhibitory neurons in neocortex. Nature 402, 75-79. (doi:10.1038/47035) · doi:10.1038/47035
[44] Beierlein M, Gibson JR, Connors BW. (2000) A network of electrically coupled interneurons drives synchronized inhibition in neocortex. Nat. Neurosci. 3, 904-910. (doi:10.1038/78809) · doi:10.1038/78809
[45] Fishell G, Rudy B. (2011) Mechanisms of inhibition within the telencephalon: ‘where the wild things are’. Annu. Rev. Neurosci. 34, 535-567. (doi:10.1146/annurev-neuro-061010-113717) · doi:10.1146/annurev-neuro-061010-113717
[46] Bem T, Rinzel J. (2004) Short duty cycle destabilizes a half-center oscillator, but gap junctions can restabilize the anti-phase pattern. J. Neurophysiol. 91, 693-703. (doi:10.1152/jn.00783.2003) · doi:10.1152/jn.00783.2003
[47] Sherman A. (1994) Anti-phase, asymmetric and aperiodic oscillations in excitable cells-I. Coupled bursters. Bull. Math. Biol. 56, 811-835. (doi:10.1016/S0092-8240(05)80292-7) · doi:10.1016/S0092-8240(05)80292-7
[48] Tsaneva-Atanasova K, Osinga H, Riel T, Sherman A. (2010) Full system bifurcation analysis of endocrine bursting models. J. Theor. Biol. 264, 1133-1146. (doi:10.1016/j.jtbi.2010.03.030) · doi:10.1016/j.jtbi.2010.03.030
[49] Belykh V, Belykh I, Hasler M. (2004) Connection graph stability method for synchronized coupled chaotic systems. Physica D 195, 188-206. (doi:10.1016/j.physd.2004.03.013) · Zbl 1098.82621 · doi:10.1016/j.physd.2004.03.013
[50] Belykh I, Belykh V, Hasler M. (2006) Synchronization in asymmetrically coupled networks with node balance. Chaos 16, 015102. (doi:10.1063/1.2146180) · Zbl 1144.37318 · doi:10.1063/1.2146180
[51] Belykh I, Belykh V, Hasler M. (2006) Generalized connection graph stability method for synchronization in asymmetrical networks. Physica D 224, 42-51. (doi:10.1016/j.physd.2006.09.014) · Zbl 1118.34044 · doi:10.1016/j.physd.2006.09.014
[52] Kramer MA, Traub RD, Kopell NJ. (2008) New dynamics in cerebellar Purkinje cells: torus canards. Phys. Rev. Lett. 101, 068103. (doi:10.1103/PhysRevLett.101.068103) · doi:10.1103/PhysRevLett.101.068103
[53] Belykh I, Hasler M, Lauret M, Nijmeijer H. (2005) Synchronization and graph topology. Int. J. Bifurcation Chaos 15, 3423-3433. (doi:10.1142/S0218127405014143) · Zbl 1107.34047 · doi:10.1142/S0218127405014143
[54] Wolf A, Swift JB, Swinney HL, Vastano JA. (1985) · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9
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